用户名: 密码: 验证码:
浅埋地下结构地震反应分析及设计方法研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
地下轨道交通,作为城市公共交通的重要形式,是解决城市交通问题的根本出路。以北京市为例,按照2050年的轨道交通线长期规划,轨道交通总里程将超过1000km;大规模的轨道交通建设导致近接既有建(构)筑物施工的工程大量出现,必然会出现地铁地下结构形式的多样化及空间结构的组合,地铁地下结构的日趋复杂必定给地下轨道交通结构的抗震性能提出更高的要求。本文针对目前城市地铁地下结构超近距并行、立体交叉穿越等复杂组合结构的抗震性能进行系统的分析研究,对北京地区地下轨道交通结构的抗震设计方法进行归纳、分析及分类,总结出普遍性和适用性规律,进一步提炼、改进相关设计计算方法,并结合现有规范和指南对地下各种复杂结构进行地震安全性评价,无疑对丰富地下结构抗震理论及工程抗震设计具有非常重要的意义。
     本文依托国家―973‖计划项目―城市地下基础设施的地震破坏与抗震理论‖(2007CB714203)、国家自然科学基金重点项目―城市大型地下结构强震动力灾变机理及过程模拟研究‖(90715035)、北京市自然科学基金重点项目―地铁车站立体交叉结构地震响应及抗震设计方法研究‖(8111001),基于北京地层、地下结构条件,对地铁地下轨道交通结构的抗震分析方法、地铁地下轨道交通结构的抗震设计方法适用性、改进反应位移法、地下复杂组合结构动力分析、地铁结构地震安全性评价等问题展开研究。具体的研究内容和取得的成果如下:
     (1)分析和阐明已有常用地下结构地震反应分析方法及计算流程,为地下结构抗震设计方法提供理论依据;
     (2)介绍地铁地下结构地震土压力及设计荷载条件,着重介绍适用于地下结构的简化地震土压力公式、张建民地震土压力方法;详细介绍动力时程分析方法、反应位移法、整体式反应位移法、强制反应位移法、简化地震土压力方法、反应加速度法、地下结构Pushover分析方法等地铁地下结构抗震设计方法;通过算例对各种设计方法做了综合性的比较,并为各种设计方法计算结果的差异性规律提供一定的依据;
     (3)在确定地层反应位移的三种常用方法基础上,对地层反应位移的确定进行改进及验证,提出了一种考虑地层参数及覆土厚度,并可确定地表峰值位移的计算方法,该法可反映地层等效惯性加速度的。可令地表等效惯性加速度值等于地表峰值加速度,继而可通过公式得到地表峰值位移,最终得到地层的反应位移,与既有的国内各类抗震设计规范有了很好的衔接;其次,对软硬交界地层、近断层地层等复杂地层下的地下结构变形及受力进行规律性的分析研究,以对复杂地层下地下结构反应位移法的计算提供修正依据;最后将薄层单元分析法求解得到的地下结构地层阻抗函数运用到地下结构反应位移法中,以快速而准确确定地层动弹簧刚度;
     (4)以FLAC及FLAC3D为计算工具,进行不同距径比的双孔并行隧道地震动力响应分析、对不同角度下双孔并行隧道地震动力响应分析、推导等速运行荷载下上下并行双层隧道的稳态振动的解析解、对不同间距地铁地下交叉结构动力响应分析、对竖向强震作用下密贴地铁地下交叉结构动力响应分析,从而地铁地下复杂组合结构的动力特性规律系统的归纳总结。
     (5)根据《市政公共设施抗震设防专项论证技术要点(地下工程篇)》、《城市轨道交通结构抗震设计规范》(征求意见稿-2011)、《建筑抗震设计规范》(GB50011-2010)、《城市地下轨道交通工程抗震设防指南》(征求意见稿-2012)等相关规范及国内外学者的研究成果,以具体的地铁线路为案例,在设计风险源的基础上合理的辨识地震风险源,并根据典型的地震风险源的地质条件、结构形式进行抗震分析,总结出普遍性规律,对工程实际抗震设计与施工具有重要的意义,同时也为以后类似工程提供借鉴。
As an important form of urban public transport, underground mass transit cansolve the urban transport problems effectively and efficiently. Taken Beijing as anexample, total mileage will exceed1000km in the future according to the long-termplanning in2050. Large-scale construction of rail transit lines lead to the occurrenceof large-scale construction of approaching existing building (structures), which willinevitably lead to the appearance of diversity and spatial composition of subwaystructures. The increasing complexity of the subway structures demands higherrequirement of seismic performance. Therefore, seismic performance analysis of thecomplex composite structures, such as extremely close approaching parallel andintersecting subway structures; summary, classification and analysis o f Beijing'sunderground subway structure seismic design methods, of which universal andapplicable laws can be summed up, and these methods are then developed andimproved. Finally, seismic safety of underground complex structures is evaluated incombination with all related standard and guidelines. Therefore, it may have greatsignificance on seismic design and theories of underground structures.
     This research is supported by National Program on Key Basic Research Project(973Program): Earthquake damage of urban underground infrastructure and seismictheory, supported by Natural Science Foundation: research on urban large-scaleearthquake disaster mechanism of underground structures and process simulation, andsupported by Natural Science Foundation of Beijing: Study on seismic response ofthree-dimensional intersected underground subway structures and its seismic designmethod. Based on strata and underground structures in Beijing, seismic analysismethods of the of subway structures, applicability of seismic design methods ofsubway structures, improved response displacement method, dynamic analysis ofcomplex composition of subway structures and seismic safety evaluation of subwaystructures The principal study contents and results are as follows:
     (1) Seismic analysis methods of subway structures are introduced and clarifiedwith their calculation procedures, which provide theoretical basis for seismic designmethods.
     (2) Underground earth pressure and seismic design load conditions are introduced,especially the simplified seismic earth pressure formula, Zhang Jianmin‘s seismicearth pressure method, and meanwhile seismic design methods for subway structuresare introduced, including dynamic time history analysis method, responsedisplacement method, integrated response displacement method, modified crosssection racking deformation method, the response acceleration method and Pushoveranalysis method, the results of which are compared and analyzed through a instance,providing some reference for the difference law of various design methods‘results.
     (3) Based on the three methods of determining stratum response displacement, an improvement method is proposed which considers the stratum parameters and depthof soil. It can reflect the determination of ground surface peak displacement of groundmotion parameters using equivalent inertia acceleration. Then deformation and stressregularity of underground structures in hard and soft layered strata, near-fault strataand etc. are analyzed, which provide reference for the modification of responsedisplacement method of underground structures in complex strata. Impedancefunction of underground structures obtained by thin layer method (TLM) is applied tothe response displacement method in order to quickly and accurately determines thespring stiffness of the strata.
     (4) The finite difference procedure FLAC and FLAC3D is used to simulate andanalyze seismic response characteristics of double holes parallel tunnels of differentratio of distance to diameter and different angles. The analytic solutions of the steadyvibration of upper and lower parallel double tunnel are obtained under a moving loadwith uniform velocity. The seismic response characteristics of intersectingunderground subway structures of different spacing and closely-attached intersectingunderground subway structures under vertical strong ground motion are studied inorder to summarize systematically dynamic characteristics of complex composition ofsubway structures.
     (5) According to ,(draft-2011),(GB50011-2010),(draft-2012) and other relevant standardsand research results at home and abroad, a specific subway structure is taken as anexample to identify risk sources. Then according to the typical geological andstructural conditions, seismic response characteristics are analyzed and universal lawis summed up, which has significance and provides a reference for similar projects.
引文
1钱七虎.现代城市地下空间开发利用技术及其发展趋势[J].铁道建筑技术,2000(5):1-6.
    2钱七虎.岩土工程的第四次浪潮[J].地下空间,1999,19(4):267-272.
    3施仲衡,王新杰,沈子钧.解决我国大城市交通问题的根本途径——稳步发展地铁与轻轨交通[J].都市快轨交通,1996(1):2-5.
    4刘晶波,李彬.地铁地下结构抗震分析及设计中的几个关键问题[J].土木工程学报,2006,39(6):106-110.
    5张建民,刘晶波,宋二祥等.高烈度地震环境下北京地铁地下结构抗震设计与对策研究[R].北京:清华大学土木水利学院,2004.
    6李彬.地铁地下结构抗震理论分析与应用研究[D].北京:清华大学博士学位论文,2005.
    7孙钧.岩土力学与地下工程结构分析计算的若干进展[J].力学季刊,2005,26(3):329-338.
    8钱七虎,陈晓强.利用地下空间建设―花园城市‖[J].地下空间,2003,23(3):302-305.
    9张晓丽.浅埋暗挖下穿既有地铁构筑物关键技术研究与实践[D].北京交通大学博士学位论文.2007:5~2526~98.
    10许有俊.浅埋暗挖地铁隧道上穿既有线结构关键问题研究[D].北京工业大学博士学位论文.2011:3~4.
    11Hamidreza R, Hossein S J. The bam (Iran) earthquake of December26,2003: From anengineering and seismological point of view. Journal of Asian Earth Scienc e,2006,27(5):576-584.
    12Bhalla S, Yang Y W, Zhao J, et al. Structural health monitoring of undergroundfacilities-technological issues and challenges[J]. Tunnelling and Underground SpaceTechnology,2005,20(5):487-500.
    13Liu H B(刘华北), Song E X(宋二祥). Seismic response of large underground structures inliquefiable soils subjected to horizontal and vertical earthquake excitations[J]. Computers andGeotechnics,2005,32(4):223-244.
    14Wang W L, Wang T T, Su J J, et al. Assessment of damage in mountain tunnels due to theTaiwan Chi-Chi Earthquake[J]. Tunnelling and Underground Space Technology,2001,16(3):133-150.
    15Scawthorn C, Johnson G S. Preliminary report: Kocaeli (Izmit) earthquake of17August1999[J]. Engineering Structure,2000,22(7):727-745.
    16周云,汤统壁,廖红伟.城市地下空间防灾减灾回顾与展望[J].地下空间与工程学报,2006,2(3):467-474.
    17王秀英,刘维宁,张弥.地下结构震害类型及机理研究[J].中国安全科学学报,2003,13(11):55-58.
    18季倩倩,杨林德.地下铁道震害与震后修复措施[J].灾害学,2001,16(2):31-36.
    19王文礼,苏灼谨,林峻弘.台湾集集大地震山岳隧道受损情性之探讨[J].现代隧道技术,2001,38(2):52-60.
    20Youssef M.A. Hashasha, Jeffrey J. Hooka, Birger Schmidtb, John I-Chiang Yao, Seismicdesign and analysis of underground structures[J], Tunneling and Underground SpaceTechnology,2001, Vol.16:247~293.
    21于翔,赵跃堂,郭志昆,人防工程的抗地震问题[J],地下空间,2001,21(1):28~32
    22陈国兴.岩土地震工程学[M],北京,科学出版社,2007.
    23宋胜武.汶川大地震工程震害分析与研究[M],北京,科学出版社,2009.04.
    24陶连金等.5.12汶川大地震后震区城市轨道交通调研报告,中国土木工程学会城市轨道交通技术推广委员会,2008,6.
    25中华人民共和国行业标准.关于印发《市政公共设施抗震设防专项论证技术要点(地下工程篇)》的通知(建质[2011]13号)[S].北京:中华人民共和国住房和城乡建设部,2011.
    26中华人民共和国行业标准.城市轨道交通结构抗震设计规范(征求意见稿-2011)[S].北京:中华人民共和国住房和城乡建设部,2011.
    27中华人民共和国行业标准.建筑抗震设计规范(GB50011-2010)[S].北京:中华人民共和国住房和城乡建设部,2010.
    28中华人民共和国行业标准.城市地下轨道交通工程抗震设防指南(征求意见稿-2011)[S].北京:中华人民共和国住房和城乡建设部,2011.
    29上海市工程建设规范.地下铁道建筑结构抗震设计规范[S],同济大学,2008.
    30上海市地铁区间隧道和车站的地震灾害防治对策研究(DG/TJ08--2008).
    31林皋,梁青槐.地下结构的抗震设计[J].土木工程学报,1996,29(1).
    32黄先锋.地下结构的抗震计算-位移响应法[J].铁道建筑,1999,(6):3-6.
    33边金,陶连金,张印涛.地下结构抗震设计方法的比较与分析[J].现在隧道技术,2008,45(6).
    34韩大建,周阿兴.沉管隧道地震响应分析的等效质点系模型探讨[J].华南理工大学学报,1999,27(11).
    35孙钧,候学渊.地下结构(上、下册).北京:科学出版社,1987.
    36Michael O‘Rouker,Leon R.L.Wang,谢君斐等译.地震工程与土动力学问题译文集.北京:地震出版社,1985.
    37Newmark, N.M.. Problems in wave propagation in soil and rock. Proceedings of theInternational Symposium on Wave ropagation and Dynamic Properties of EarthMaterials,1968.
    38Kuesel, T.R. Earthquake Design Criteria for Subways. J.Struct. Div., ASCE ST6,1969:1213-1231.
    39小泉淳,张稳军,袁大军.盾构隧道的抗震研究及算例[M].中国建筑工业出版社,2009.9.
    40Okamoto, S., Tamura, C., Kato, K., and Hamada, M.,1973,―Behaviors of submerged tunnelsduring earthquakes,‖Proceedings of the Fifth World Conference on Earthquake Engineering,Rome, Italy,(1):544-553.
    41D.k.shukla, P.c.rizzo, and D.e.stephenson, Earthquake load analysis of tunnels and shafts,proceeding of5th world conference of earthquake engineering,1973
    42St John C M, Zahrah T F. A seismic design of underground structures. Tunneling andUnderground Space Technology,1987,2(2)165-197.
    43Power, M.S., Rosidi, D., Kaneshiro, J., Strawman: screening, evaluation, and retrofit designof tunnels. Report Draft. National Center for Earthquake Engineering Research, Buffalo,New York,1996, Vol. III.
    44Power, M., Rosidi, D., Kaneshiro, J., Seismic vulnerability of tunnels-revisited. In: Ozedimir,L., Ed.. Proceedings of the North American Tunneling Conference. Elsevier, Long Beach,CA, USA,1998.
    45Penzien, J.,2000,―Seismically indueced racking of tunnel linings,‖[J], EarthquakeEngineering and Structural Dynamics, Vol.29, pp.683-691.
    46Penzien, J. and Wu, C.,1998,―Stresses in linings of bored tunnels,‖[J],EarthquakeEngineering and Structural Dynamics, Vol.27, pp.283-300.
    47Wang, J.N.,1993,―Seismic design of tunnels: a state-of-the-art approach,‖[J], Monograph7,Parsons Brinckerhoff Quade and Douglas Inc., New York.
    48Choi J S, Lee J S, Kim J M. Nonlinear earthquake response analysis of2-D undergroundstructures with soil-structure interaction including separation and sliding at interface [A].15th ASCE Engineering Mechanics Conference [C], June2-5,2002, Columbia Univers ity,New York, NY,1~8
    49Huo Hong-bin, Bobet A. Seismic design of cut and cover rectangular tunnels-evaluation ofobserved behavior of Dakai station during Kobe earthquake,1995[A]. Proceedings of1stWorld Forum of Chinese Scholars in Geotechnical Engineering, August20-22,2003[C],Tongji University, Shanghai,456~466.
    50刘晶波,李彬,谷音等。地铁盾构隧道地震反应特性研究[J].现代隧道技术(增刊)2004,4:251~257.
    51李彬,刘晶波,尹骁.双层地铁车站的强地震反应分析[J].地下空间与工程学报,2005,1(5):779-782.
    52Chen Guo-xing, Zhuang Hai-yang. Analysis on the earthquake response of subway stationbased on the substructure subtraction method[A]. Proceedings of the Third InternationalConference on Earthquake Engineering [C].19~20October,2004, Nanjing P. R. China,195-199.
    53刘如山.强地震动作用下地铁结构与土脱开滑移的研究[J].地震工程与工程振动,2004,24(6):136~141.
    54刘如山,胡少卿,石宏彬.地下结构抗震计算中拟静力法的地震荷载施加方法研究[J].岩土工程学报,2007,29(2):237-242.
    55刘智勇,郑永来.矩形断面地下结构抗震设计简化方法探索[J].结构工程师,2008,24(2):6-10.
    56刘晶波,李彬.地铁地下结构抗震分析及设计中的几个关键问题[J].工程力学,2006,39(6):106-110.
    57刘晶波,李彬,刘祥庆:地下结构抗震设计中的静力弹塑性分析方法[J].土木工程学报,2007,40(7):68-76.
    58刘晶波,刘祥庆,薛颖亮.地下结构抗震分析与设计的Pushover方法适用性研究[J].工程力学,2009,26(1):49-57.
    59耿萍,何川,晏启祥.盾构隧道纵向地震响应分析[J].西南交通大学学报,2007,42(3):283-287.
    60卢志杰.隧道受震反应分析之研究[D].台湾:国立中央大学,2009.
    61蒋通,宋晓星.层状地层中埋管地基阻抗函数的分析方法[J].力学季刊,2009,30(2):243-249.
    62蒋通,宋晓星.用薄层法分析层状地层条形基础的阻抗函数[J].力学季刊,2009,30(1):62-70.
    63陈磊,陈国兴.近场和远场地震动作用下双层竖向重叠地铁隧道的地震反应比较[J].中国铁道科学,2010,31(1):79-85.
    64姜忻良,谭丁,姜南.交叉隧道地震反应三维有限元和无限元分析[J].天津大学学报,2004,37(4):307-311.
    65陈磊,陈国兴,龙慧.地铁交叉隧道近场强地震反应特性的三维精细化非线性有限元分析[J].岩土力学,2010,31(12):3971-3976.
    66于翔,钱七虎,赵跃堂,郭志昆.地铁工程结构破坏的竖向地震力影响分析[J].解放军理工大学学报(自然科学版),2001,2(3):75-77.
    67曹炳政,罗奇峰,马硕,刘晶波.神户大开地铁车站的地震反应分析[J].地震工程与工程振动,2002,22(4):102-107.
    68KIRCHER C A. Kobe Earthquake: Ground Shaking, Damage and Loss [C]//Proceedingsof the14th St ructures Congress: Part2(of2). Chicago: ASCE,1996.
    69熊良宵,李天斌,刘勇.隧道地震响应数值模拟研究[J].地质力学学报,2007,13(3):255-260.
    70陶连金,王文沛等.竖向强震作用下密贴地铁地下交叉结构动力响应分析[J].岩土工程学报,2012.
    71M. Celebi, J. Lysmer, J. E. Luco, Recommendations for a soil-structure interactionexperiment report based on a workshop held at San Francisco[N], California on February7,1992
    72G. Gazetas, N. Gerolymos, I. Anastasopoulos, Response of three Athens metro undergroundstructures in the1999Parnitha earthquake[J], Soil Dynamics and Earthquake Engineering
    2005(25):617~633
    73Jun Matsui, Keizo Ohtomo, Kensei Kanaya, Development and validation of nonlineardynamic analys is in seismic performance verification of underground RC structures[J],Journal of advanced concrete technology,2004, Vol.2:25~35
    74季倩倩。地铁车站结构振动台模型试验研究[D],同济大学博士学位论文,2002:15~34
    75宫必宁,赵大鹏.地下结构与土动力相互作用试验研究[J],地下空间,2002,22(4):320~326
    76庄海洋.土-地下结构非线性动力相互作用及大型振动台试验研究[D],南京工业大学博士学位论文,2006:2~8
    77陶连金,王沛霖,边金.典型地铁车站结构振动台模型试验[J].北京工业大学学报,2006,32(9):798-801
    78陈国兴,庄海洋,程绍革,杜修力等.土-地铁隧道动力相互作用的大型振动台试验:试验方案设计[J].地震工程与工程振动,2006,26(6):178-183
    79陈国兴,庄海洋,杜修力等.土-地铁隧道动力相互作用的大型振动台试验:试验结果分析[J].地震工程与工程振动,2007,27(1):164-170
    80陈国兴,庄海洋,杜修力等.液化场地土-地铁车站结构大型振动台模型试验研究[J].地震工程与工程振动,2007(3):163-170
    81庄海洋,陈国兴,杜修力等.液化大变形条件下地铁车站结构动力反应大型振动台试验研究[J].地震工程与工程振动,2007(4).
    82Choshiro Tamura and Shunzo Okamoto. On Earthquake Resistant Design of a SubmergedTunnel[C]. International Symposium on Earthquake Structure Engineering. St. Louis,Missouri, USA, Aug.1976.
    83阎盛海.地下结构抗震[M].大连理工大学出版社,1989.
    84严松宏.地下结构随机地震响应分析及其动力可靠度研究[D].西南交通大学博士学位论文.2003
    85耿萍,何川,晏启祥.水下盾构隧道抗震设计分析方法的适应性研究[J].岩石力学与工程学报,2007,26(2).
    86Hashash, Y.M.A., Hook, J.J., Schmidt, B., and Yao, J.I.C.,2001,―Seismic design andanalysis of underground structures,‖Tunneling and Underground Space Technology, Vol.16,pp.247-293.
    87陈仲颐,王洪瑾,周景星.土力学[M].清华大学出版社,1994.
    88北京金土木软件技术有限公司. SAP2000中文版使用指南.北京:人民交通出版社,2006.
    89王文沛,陶连金,张波,李文博,魏云杰.一种计算地下结构地震主动土压力的新方法[J].防灾减灾工程学报,2010,30(6):620-623.
    90Zhang JM, Shamoto Y, Tokimatsu K,1998.―Evaluation of earth pressure under any lateraldeformation,‖[J], Soils and Foundations, Vol.38,No.1pp.15-33.
    91Zhang JM, Shamaoto Y, TokimatsuK,.1998. Seismic earth pressure theory for retainingwalls under any lateral displacement,‘[J]. Soils and Foundations, Vol.38,No.2pp.143-163.
    92Harvey W. Parker, Underground space: Good for sustainable development, and vice versa,International tunneling association open session world tunnel congress, Singapore, May,2004
    93Hidenao Hayashi, Tamotsu Marui, Nobuhiko Taniguchi, Shigeru Kayano, Restoration ofHanshin expressway after Kobe/Awaji earthquake challenge of623days before opening,Cement&concrete composites,2000,22(2):29-38
    94M. Celebi, J. Lysmer, J. E. Luco, Recommendations for a soil-structure interactionexperiment report based on a workshop held at San Francisco, California on February7,1992
    95Itasca Consulting Group,Inc.. Fast Language Analysis of continua in2dimensions, version5.0, user‘s manual. Itasca Consulting Group, Inc.,2005.
    96刘晶波,王文晖,赵冬冬.地下结构横截面抗震设计分析方法综述[J].施工技术,2010,39(6):91-95.
    97日本铁道构造物等设计标准及解说[S],中国铁道出版社,2003.
    98日本沉管隧道抗震设计细则[S],日本土木工程协会,1995.
    99关于当前新建构筑物抗震设计的参考资料[R].日本财团法人铁道综合技术研究所.
    100大型地下结构的抗震设计指南[S],日本建设部土木研究所地震防灾部抗震研究室,1992.
    101台北都会区捷运系统工程-土木工程设计手册[S].台北市政府捷运工程局,2002.
    102川岛一彦.地下构筑物の耐震设计[M].日本:鹿岛出版会,1994.
    103陶连金,王文沛,张波等.近断层地震动破裂向前方向性与滑冲效应对典型地铁车站结构动力响应的影响[J].地震工程与工程振动学报,2011,31(6):38-44.
    104王海云,谢礼立.近断层强地震动的特点[J].哈尔滨工业大学学报,2006,38(12):2070-2076.
    105杨迪雄,赵岩.近断层地震动破裂向前方向性与滑冲效应对隔震建筑结构抗震性能的影响.地震学报,2010,32(5):579-587.
    106刘启方,袁一凡,金星,丁海平.近断层地震动的基本特征[J].地震工程与工程振动,2006,26(1):1-10.
    107杨迪雄,赵岩,李刚.近断层地震动运动特征对长周期结构地震响应的影响分析[J].防灾减灾工程学报,2007,27(2):133-140.
    108刘祥庆,刘晶波.基于纤维模型的拱形断面地铁车站结构弹塑性地震反应时程分析[J].工程力学,2008,25(10):150-157.
    109陈磊,陈国兴.近断层强地震动下双层竖向重叠地铁隧道的地震反应[J].防灾减灾工程学报,2008(4):399-408.
    110刘洋.近断层地铁隧道地震作用下动力响应数值模拟研究[D].北京:北京交通大学,2009:70-85.
    111Kalkan E, Kunnath S K. Effects of fling step and forward directivity on seismic response ofbuildings[J]. Earthquake Spectra,2006,22(2):367-390.
    112边金,陶连金,王文沛,张波.地震作用下地铁车站结构的动力变形响应研究[J].防灾减灾工程学报,2010,30(4):393-397.
    113陶连金,孙斌,李晓霖.超近距离双孔并行盾构施工的相互影响分析[J].岩石力学与工程学报,2009,28(9):1856-1861.
    114陈先国,王显军.近距离重叠隧道的二维和三维有限元分析[J].西南交通大学学报,2003,38(6):643-646.
    115周斌.近接盾构隧道力学行为与近接分区研究[D].成都:西南交通大学,2009:1-10.
    116郑余朝,仇文革.重叠隧道结构内力演变的三维弹塑性数值模拟[J].西南交通大学学报,2006,41(3):376-380.
    117翟婉明.车辆—轨道耦合动力学[M].北京:中国铁道出版社,2007.
    118邢书珍.铁路轨道振动的理论[J].中国铁道科学.1980(I).
    119余占奎.软土盾构隧道纵向设计方法研究[D],同济大学研究生博士学位论文,2006.12.
    120中国数学会上海分会.高次方程[M].1957.
    121谢伟平,王国波,于艳丽.移动荷载作用下双层Euler梁模型土动力响应分析[J].地震工程与工程振动,2004,24(1):82–86.
    122袁俊,吴敏哲,孟昭博等.基于双层Euler-Bernoulli梁理论的浮置板轨道隔振研究[J].西安建筑科技大学学报(自然科学版),2009,41(5):683–688.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700